Question

Mike Powell holds the record for the long jump of 8.95 m, established in 1991. If he left the ground at an angle of 15°, what was his initial speed?

a) 8.45 m/s
b) 9.72 m/s
c) 11.36 m/s
d) 12.84 m/s

Answer 1

Using the range formula for projectile motion, the initial speed required by Mike Powell to set the long jump world record of 8.95 m at a 15° angle is calculated to be approximately 9.72 m/s.

Step-by-step explanation:

The student has inquired about the initial speed required by Mike Powell to set the long jump world record of 8.95 m at an angle of 15°. This question is a classic problem in projectile motion, a part of physics that deals with objects that are projected into the air and are subject to gravity.

To find the initial speed, we can use the range formula for projectile motion:

R = (v^2 × sin(2θ)) / g

Where R is the range (8.95 m), v is the initial velocity, θ is the launch angle (15°), and g is the acceleration due to gravity (9.81 m/s^2). We can solve for v by rearranging the formula and input the given values:

v = √((R × g) / sin(2θ))

v = √((8.95 m × 9.81 m/s^2) / sin(30°))

v ≈ 9.72 m/s

Therefore, the correct answer is (b) 9.72 m/s.